To solve the inequality
[tex]\[ \frac{x}{6} - 2 \geq 3, \][/tex]
follow these steps:
1. Isolate the variable term:
First, we need to isolate the term involving [tex]\( x \)[/tex]. Add 2 to both sides of the inequality to achieve this:
[tex]\[
\frac{x}{6} - 2 + 2 \geq 3 + 2.
\][/tex]
Simplifying this, we have:
[tex]\[
\frac{x}{6} \geq 5.
\][/tex]
2. Eliminate the fraction:
Next, we need to get rid of the fraction by multiplying both sides of the inequality by 6 (which is the denominator):
[tex]\[
6 \cdot \frac{x}{6} \geq 6 \cdot 5.
\][/tex]
This simplifies to:
[tex]\[
x \geq 30.
\][/tex]
Therefore, the solution to the inequality [tex]\(\frac{x}{6} - 2 \geq 3\)[/tex] is:
[tex]\[
x \geq 30.
\][/tex]
